Chapter 1.1

Points, Lines, and Planes

Concept

Name Lines and Planes

A. Use the figure to name a line containing point K.

Answer: The line can be named as line a.

There are three points on the line. Any two of the points can be used to name the line.

Name Lines and Planes

B. Use the figure to name a plane containing point L.

You can also use the letters of any three noncollinear points to name the plane.plane JKM plane KLM plane JLM

Answer: The plane can be named as plane B.

A. Use the figure to name a line containing the point X.

A. line X

B. line c

C. line Z

D.

B. Use the figure to name a plane containing point Z.

A. plane XY

B. plane c

C. plane XQY

D. plane P

Example 2 Model Points, Lines, and Planes

A. Name the geometric shape modeled by a 10 12 patio.

Answer: The patio models a plane.

Example 2 Model Points, Lines, and Planes

B. Name the geometric shape modeled by a button on a table.

Answer: The button on the table models a point on a plane.

Example 2a

A. point

B. line segment

C. plane

D. none of the above

A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.

Example 2b

A. point

B. line segment

C. plane

D. none of the above

B. Name the geometric shape modeled by the ceiling of your classroom.

Intersections of lines and planes

Two lines intersect at a point.

Two planes intersect at a line.

Draw Geometric Figures

Draw a surface to represent plane R and label it.Draw a Line anywhere on the plane.Draw dots on the line for Point A and Point B.

A

B

Draw a line intersecting Line AB.Draw dots on this line for Points D and E. Label the points.

D

E

Label the intersection point of the two lines as P.

P

Draw a dot for Point C in Plane R such that it will not lie on either line. Label the point.

C

Draw Geometric Figures

There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0).

Answer:

A. B.

C. D.

A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines.

Interpret Drawings

A. How many planes appear in this figure?

Answer: There are two planes: plane S and plane ABC.

Interpret Drawings

B. Name three points that are collinear.

Answer: Points A, B, and D are collinear.

Interpret Drawings

C. Are points A, B, C, and D coplanar? Explain.

Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar.

Interpret Drawings

Answer: The two lines intersect at point A.

A. one

B. two

C. three

D. four

A. How many planes appear in this figure?

A. B, O, and X

B. X, O, and N

C. R, O, and B

D. A, X, and Z

B. Name three points that are collinear.

A. yes

B. no

C. cannot be determined

C. Are points X, O, and R coplanar?

A. point X

B. point N

C. point R

D. point A